You have a mass of 60-kg, and you are facing your friend who has a mass of 100 kg. you skate towards
each other fast, and after you collide you both come perfectly to rest. if your friend had an initial
velocity of 3 m/s, what must have been your initial velocity?

My initial velocity is 5 m/s.

Explanation:

In this case, momentum can be conserved.

initial momentum = final momentum

Since both the bodies come to rest after collision,

Final momentum = 0

Let my velocity be v, and mass, m1 = 60 kg

Friend's mass, m2 = 100 kg

Friend's velocity, v2 = 3 m/s

Intial momentum = m1v + m2v2

= 60v + 300

Conserving momentum,

60v + 300 = 0

v= -5 m/s

( Negative sign indicates that me and my friend are moving in opposite directions that is towards each other)

the bal will not change its velocity.